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Convert 5 × 4 4/5π radians to degrees.
1) 225°
2) 300°
3) 144°
4) 240°

1 Answer

1 vote

Final answer:

To convert 5 × 4 4/5π radians to degrees, we express 4 4/5 as an improper fraction, multiply by 5 to find the radian measure, then convert to degrees using the factor 1 radian ≈ 57.3°. After the calculation, the result is approximately 240°.

The correct option is 4.

Step-by-step explanation:

To convert 5 × 4 4/5π radians to degrees, first simplify the mixed number 4 4/5 to an improper fraction. The fraction 4 4/5 is equivalent to (4 × 5 + 4)/5, which simplifies to 24/5.

Next, multiply 5 by 24/5π to find the radian measure, which is 24π. Now, we can use the conversion factor 1 radian ≈ 57.3° to convert radians to degrees:

24π radians × (57.3° / 1 radian) = 24 × 3.14159 × 57.3° = 432π degrees / 1 radian.

Then, calculate 432π degrees, knowing that π is approximately 3.14159:

432 × 3.14159 = 1357.16808°

Lastly, we can identify the closest answer choice:

240°

Since 1357.16808° is closest to 1368° (which is 240° when reduced within a single revolution), the approximate answer to the conversion of 5 × 4 4/5π radians to degrees is 240°.

The correct option is 4.

User Yoaz Menda
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